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This paper is a natural continuation of cite{Kr_20_2} and cite{Kr_21_1} where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in $L_{d+1}(mathbb{R}^{d+1})$ and some properties of their Greens functions and probability of passing through narrow tubes are investigated. On the basis of this here we study some further properties of these processes such as Harnack inequality, Holder continuity of potentials, Fanghua Lin estimates and so on.
We present new conditions on the drift of the Morrey type with mixed norms allowing us to obtain Aleksandrov type estimates of potentials of time inhomogeneous diffusion processes in spaces with mixed norms and, for instance, in $L_{d_{0}+1}$ with $d_{0}<d$.
This paper is a natural continuation of cite{Kr_20_2}, where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in $L_{d+1}(mathbb{R}^{d+1})$.
We prove the solvability of It^o stochastic equations with uniformly nondegenerate, bounded, measurable diffusion and drift in $L_{d+1}(mathbb{R}^{d+1})$. Actually, the powers of summability of the drift in $x$ and $t$ could be different. Our results
In this paper we deal with the heat equation with drift in $L_{d+1}$. Basically, we prove that, if the free term is in $L_{q}$ with high enough $q$, then the equation is uniquely solvable in a rather unusual class of functions such that $partial_{t}u, D^{2}uin L_{p}$ with $p<d+1$ and $Duin L_{q}$.
This paper is a natural continuation of [8], where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in $L_{d+1}(mathbb{R}^{d+1})$. Here we st